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Reaction Coordinate
Diagrams & Transition States

Master the energy landscape of chemical reactions: activation energy, transition states, and how to read the story a reaction coordinate diagram tells.

Organic Chemistry 1

What Is a Reaction Coordinate Diagram?

A reaction coordinate diagram is a graph that plots free energy (\( G \)) on the vertical axis against the reaction progress (reaction coordinate) on the horizontal axis. It shows how the energy of a system changes as reactants transform into products.

Key Terms on the Energy Landscape

Reactants
Starting materials at their initial free energy level on the left of the diagram.
Transition State
The highest-energy point along the pathway: an unstable, fleeting geometry denoted \( [\ddagger] \).
Products
The final species formed, sitting at the energy level on the right of the diagram.

Anatomy of a One-Step Reaction

Reaction Coordinate
Free Energy (\(G\))
\( E_a \) \( \Delta G < 0 \) Reactants \( [\ddagger] \) Products

Activation Energy: \( E_a \)

Activation energy is the minimum energy input required for a reaction to proceed. It is the difference between the energy of the transition state and the energy of the reactants:

Transition State vs Intermediate

Transition State \( [\ddagger] \)
An energy maximum on the diagram. Cannot be isolated. Bonds are partially formed and partially broken simultaneously. Exists for a single molecular vibration.
Intermediate
An energy local minimum (valley) between two transition states. A real species that exists briefly. Has a finite (though often short) lifetime. Can sometimes be detected.

Two-Step Reaction: Intermediates Appear

Reaction Coordinate
Free Energy (\(G\))
Intermediate \( [\ddagger]_1 \) \( [\ddagger]_2 \) Reactants Products \( E_{a1} \) \( E_{a2} \)

The Rate-Determining Step

In a multi-step reaction, the rate-determining step (RDS) is the step with the highest activation energy. It is the tallest hill on the diagram: the bottleneck that limits how fast the overall reaction proceeds.

Exergonic vs Endergonic

Exergonic
\( \Delta G < 0 \). Products are lower in energy than reactants. Energy is released. Thermodynamically favorable.
Endergonic
\( \Delta G > 0 \). Products are higher in energy than reactants. Energy is absorbed. Not spontaneous under standard conditions.

How a Catalyst Changes the Diagram

Reaction Coordinate
Free Energy (\(G\))
Uncatalyzed Catalyzed Reactants Products Lower \( E_a \)

How to Read the Diagram

1
Count the peaks. Each peak is a transition state. The number of peaks tells you the number of elementary steps.
2
Count the valleys. Each valley between peaks is a reactive intermediate. Number of intermediates = number of peaks minus one.
3
Find the largest energy barrier. The step with the largest activation energy (\(E_a\))—the tallest climb from its own starting point—is the rate-determining step.
4
Compare start and end heights. Products lower than reactants: exergonic. Products higher: endergonic.
5
Measure \( E_a \). The vertical distance from reactants (or the preceding minimum) to the next transition state peak.

Example 1: \( \text{S}_\text{N}2 \) Reaction

Reaction Coordinate
Free Energy (\(G\))
\( [\ddagger] \) \( \text{Nu:}^- + \text{R-LG} \) \( \text{Nu-R} + \text{LG:}^- \) \( E_a \) \( \Delta G < 0 \)

Example 2: \( \text{S}_\text{N}1 \) Reaction (Two Steps)

Reaction Coordinate
Free Energy (\(G\))
Carbocation (\(\text{R}^+\)) \( [\ddagger]_1 \) \( [\ddagger]_2 \) \( \text{R-LG} \) \( \text{Nu-R} \) \( E_{a1} \) \( E_{a2} \) Step 1: Ionization Step 2: Attack

Example 3: An Endergonic Reaction

Reaction Coordinate
Free Energy (\(G\))
\( [\ddagger] \) Reactants Products \( \Delta G > 0 \) \( E_a \)

Common Mistakes to Avoid

✕ Confusing TS with Intermediate
A transition state is a maximum (peak). An intermediate is a local minimum (valley). They are not the same species.
✕ Negative \( E_a \)
Activation energy is always positive. If you calculate a negative value, you have subtracted in the wrong direction.
✕ Catalyst Changes \( \Delta G \)
A catalyst lowers \( E_a \) but does not change the thermodynamic \( \Delta G \). Start and end energy levels stay the same.

Summary Comparison

One-Step (e.g., \( \text{S}_\text{N}2 \)) Two-Step (e.g., \( \text{S}_\text{N}1 \))
Peaks 1 2
Intermediates 0 1 (carbocation, \( \text{R}^+ \))
Rate-Determining Step Only step Step with highest \( E_a \)
Transition States 1 \( [\ddagger] \) 2 \( [\ddagger]_1, [\ddagger]_2 \)
Catalyst Effect Lowers \( E_a \), does not change \( \Delta G \)

Question 1 of 5

On a reaction coordinate diagram, a transition state corresponds to:

Question 2 of 5

A reaction coordinate diagram shows three peaks. How many intermediates does the mechanism have?

Question 3 of 5

Adding a catalyst to a reaction will:

Question 4 of 5

If the products of a reaction are higher in energy than the reactants on a reaction coordinate diagram, the reaction is:

Question 5 of 5

In an \( \text{S}_\text{N}1 \) mechanism, the rate-determining step is identified on the diagram as the step with: